System and method for locating a fracture in an earth formation

ABSTRACT

The invention relates to techniques for locating and determining the orientation of a fracture in an earth formation. Systems and methods for detecting a fracture in an earth formation using a propagation tool include producing electromagnetic fields using a TMD transmitter in the tool; measuring corresponding voltage signals detected with one or more TMD receivers in the tool; determining harmonics from the measured signal responses by shifting the responses (e.g. by 90 degrees) and performing an addition or subtraction using the shifted response. In some embodiments, the second harmonic is processed to determine the fracture orientation.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to the field of subsurface explorationand, more particularly, to logging techniques for detecting and locatingfractures in earth formations.

[0003] 2. Description of Related Art

[0004] Electromagnetic (EM) logging tools have been employed in thefield of subsurface exploration for many years. These logging tools orinstruments entail an elongated support equipped with antennas that areoperable as sources or sensors. The antennas on these tools aregenerally formed as loops or coils of conductive wire. In operation, atransmitter antenna is energized by an alternating current to emit EMenergy through the borehole fluid (“mud”) and into the surroundingformations. The emitted energy interacts with the borehole and formationto produce signals that are detected and measured by one or morereceiver antennas. The detected signals reflect the interaction with themud and the formation. By processing the detected signal data, a log orprofile of the formation and/or borehole properties is determined.

[0005] Conventional EM logging techniques include “wireline” logging andlogging-while-drilling (LWD) or measurement-while-drilling (MWD).Wireline logging entails lowering the instrument into the borehole atthe end of an electrical cable to obtain the subsurface measurements asthe instrument is moved along the borehole. LWD/MWD entails attachingthe instrument disposed in a drill collar to a drilling assembly while aborehole is being drilled through earth formations. A developing method,sometimes referred to as logging-while-tripping (LWT), involves sendinga small diameter “run-in” tool through the drill pipe to measure thedownhole properties as the drill string is extracted or tripped out ofthe hole.

[0006] A coil or loop-type antenna carrying a current can be representedas a magnetic dipole having a magnetic moment strength proportional tothe product of the current and the area encompassed by the coil. Themagnetic moment direction can be represented by a vector perpendicularto the plane of the coil. In the case of more complicated coils, whichdo not lie in a single plane (e.g. saddle coils as described inpublished U.S. Patent Application Ser. No. 20010004212 A1, publishedJun. 21, 2001), the direction of the dipole moment is given by: r×dl andis perpendicular to the effective area of the coil. This integralrelates to the standard definition of a magnetic dipole of a circuit.See J. A. Stratton, ELECTROMAGNETIC THEORY, McGraw Hill, New York, 1941,p. 235, FIG. 41. Integration is over the contour that defines the coil,r is the position vector and dl is the differential segment of thecontour.

[0007] In conventional EM logging tools, the transmitter and receiverantennas are typically mounted with their axes along, or parallel, tothe longitudinal axis of the tool. Thus, these instruments areimplemented with antennas having longitudinal magnetic dipoles (LMD). Anemerging technique in the field of well logging is the use of tools withtilted or transverse antennas, i.e., where the antenna's axis is notparallel to the support axis. These tools are thus implemented withantennas having a transverse or tilted magnetic dipole moment (TMD). Onelogging tool configuration comprises triaxial antennas, involving threecoils with magnetic moments that are not co-planar. The aim of these TMDconfigurations is to provide EM measurements with directed sensitivity.Logging tools equipped with TMDs are described in U.S. Pat. Nos.6,044,325, 4,319,191, 5,115,198, 5,508,616, 5,757,191, 5,781,436 and6,147,496.

[0008] EM propagation tools measure the resistivity (or conductivity) ofthe formation by transmitting radio frequency signals into the formationand using spaced-apart receivers to measure the relative amplitude andphase of the detected EM signals. These tools transmit the EM energy ata frequency in the range of about 0.1 to 10 MHz. A propagation tooltypically has two or more receivers disposed at different distances fromthe transmitter(s). The signals reaching the receivers travel differentdistances and are attenuated to different extents and are phase-shiftedto different extents. In analysis, the detected signals are processed toderive a magnitude ratio (attenuation) and phase difference (phaseshift). The attenuation and phase shift of the signals are indicative ofthe conductivity of the formation. U.S. Pat. Nos. 4,899,112 and4,968,940 describe conventional propagation tools and signal processing.

[0009] In addition to the formation resistivity, identification ofsubsurface fractures is important in hydrocarbon exploration andproduction. Fractures are cracks or breakages within the rocks orformations. Fractures can enhance permeability of rocks or earthformations by connecting pores in the formations. Fractures may befilled with formation fluids, either brine or hydrocarbons. If afracture is filled with hydrocarbons, it will be less conductive, i.e.,a resistive fracture. Wells drilled perpendicularly to resistivefractures tend to be more “productive” (i.e., produce lager quantitiesof hydrocarbons). Thus, the determination of a resistive fracture'sorientation may help improve oil and gas production. In addition, theorientation of a fracture provides the direction of principal stress,which affects the stability of the well and it helps in predicting whichwell trajectory will be the most stable. Knowledge of fractureorientations also aids in the prediction of fracture strengths of theearth formation. Furthermore, the presence of fractures may indicatethat the mud weight used for drilling the well is too high so as tocause fracture of the rock.

[0010] Methods and systems have been developed for detecting fracturesand determining their orientation. For example, U.S. Pat. No. 3,668,619describes the rotation of a logging tool having a single acoustictransducer that senses the reflected acoustic energy to detectfractures. U.S. Pat. No. 5,121,363 describes a method for locating asubsurface fracture based on an orbital vibrator equipped with twoorthogonal motion sensors and an orientation detector. U.S. Pat. No.4,802,144 uses the measurement of hydraulic impedance to determinefractures. U.S. Pat. No. 2,244,484 measures downhole impedance to locatefractures by determining propagation velocity.

[0011] There remains a need for improved techniques for detecting andlocating fractures, and for determining their orientations, particularlyusing propagation-type tools.

SUMMARY OF THE INVENTION

[0012] The invention provides a method for locating a fracture in anearth formation using a propagation tool disposed in a boreholetraversing the formation, the tool having a longitudinal axis. Themethod comprises transmitting electromagnetic energy from a transmitterantenna disposed on the propagation tool with its magnetic moment at anangle with respect to the longitudinal tool axis; measuring voltagesignals detected at a plurality of receiver antennas disposed on thepropagation tool with their axes at an angle with respect to thelongitudinal tool axis and oriented in different directions from oneanother, the voltage signals being related to the transmittedelectromagnetic energy; associating the measured voltage signals with aplurality of azimuthal angles; and shifting at least one of the measuredvoltage signals by a predetermined angle and processing the shifted andunshifted signals to locate the fracture.

[0013] The invention provides a system for locating a fracture in anearth formation. The system comprises a propagation tool having alongitudinal axis and adapted for disposal within a borehole traversingthe formation; a transmitter antenna disposed on the tool with itsmagnetic moment at an angle with respect to the tool axis; a pluralityof receiver antennas disposed on the tool with their axes at an anglewith respect to the tool axis and oriented in different directions fromone another, the antennas adapted to detect voltage signals associatedwith electromagnetic energy transmitted by the transmitter antenna;processing means to measure the voltage signals detected by saidreceiver antennas; processing means to associate the measured voltagesignals with a plurality of azimuthal angles; and processing means toshift at least one of the measured voltage signals by a predeterminedangle and to process the shifted and unshifted signals to locate thefracture.

[0014] The invention provides a method for locating a fracture in anearth formation penetrated by a borehole. The method comprises moving apropagation tool in the borehole, the tool having a longitudinal axisand including a first transmitter antenna disposed thereon with itsmagnetic moment at a right angle to the tool axis and a plurality ofreceiver antennas disposed thereon with their axes at right angles tothe tool axis; transmitting electromagnetic energy using the firsttransmitter antenna; measuring voltage signals detected at the pluralityof receiver antennas, the signals being related to the transmittedelectromagnetic energy; associating the measured signals with aplurality of azimuthal angles; shifting at least one of the measuredsignals by a predetermined angle; and locating the fracture using theshifted and unshifted signals.

[0015] The invention provides a method for locating a fracture in anearth formation using a logging tool disposed in a borehole traversingthe formation, the tool having a longitudinal axis. The method comprisestransmitting electromagnetic energy from a transmitter antenna disposedon the tool with its magnetic moment at an angle with respect to thelongitudinal tool axis; measuring voltage signals detected with areceiver antenna disposed on the tool with its axis at an angle withrespect to the longitudinal tool axis, the voltage signals being relatedto the transmitted electromagnetic energy; determining a second harmonicassociated with the measured voltage signals; and performing acalculation on the second harmonic to locate the fracture.

[0016] The invention provides a system for locating a fracture in anearth formation. The system comprises a logging tool having alongitudinal axis and adapted for disposal within a borehole traversingthe formation; a transmitter antenna disposed on the tool with itsmagnetic moment at an angle with respect to the tool axis; a receiverantenna disposed on the tool with its axis at an angle with respect tothe tool axis, the antenna adapted to detect voltage signals associatedwith electromagnetic energy transmitted by the transmitter antenna;processing means to determine a second harmonic associated with voltagesignals detected with the receiver antenna; and processing means toperform a calculation on the second harmonic to locate the fracture.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1 is perspective view of an earth formation having a fractureand penetrated by a borehole.

[0018]FIG. 2 shows a prior art triaxial electromagnetic logging toolsuitable for practicing embodiments of the invention disposed in aborehole.

[0019]FIG. 3 is a schematic showing a logging tool disposed in aborehole (not shown) with an antenna having its axis aligned with theplane of a facture.

[0020]FIG. 4 is a schematic showing the logging tool of FIG. 3 disposedwith the antenna axis at an angle (φ) away from the plane of a facture.

[0021]FIG. 5 shows the response (Voltage and Phase) to a fracture as afunction of tool orientation with respect to the fracture (φ) measuredwith a parallel transverse antenna pair according to the invention.

[0022]FIG. 6 is a schematic diagram of an antenna configuration with onetransmitter and two receivers tilted in the transverse (XY) planeaccording to an embodiment of the invention.

[0023]FIG. 7A shows the responses (Attenuation) to a fracture as afunction of rotational azimuthal angles detected with a propagation toolaccording to the invention.

[0024]FIG. 7B shows the responses (Phase Shift) to a fracture as afunction of rotational azimuthal angles detected with a propagation toolaccording to the invention.

[0025]FIG. 8A shows the responses (Attenuation) to a fracture as afunction of rotational azimuthal angles detected with a propagation toolaccording to the invention.

[0026]FIG. 8B shows the responses (Phase Shift) to a fracture as afunction of rotational azimuthal angles detected with a propagation toolaccording to the invention.

[0027]FIG. 9 is a schematic diagram of an antenna configuration with twotransmitters and four receivers tilted in the transverse (XY) planeaccording to an embodiment of the invention.

[0028]FIG. 10 is a schematic diagram of an antenna configuration withtwo transmitters and two receivers tilted in the transverse (XY) planeaccording to an embodiment of the invention.

[0029]FIG. 11 shows the responses (Attenuation) to a fracture as afunction of rotational azimuthal angles detected with a TMD propagationtool according to the invention.

[0030]FIG. 12 shows the responses (Phase Shift) to a fracture as afunction of rotational azimuthal angles detected with a TMD propagationtool according to the invention.

[0031]FIG. 13 shows the voltage harmonics corresponding to the responsefrom FIG. 5.

[0032]FIG. 14A shows a perspective view of a formation having a boreholeand a fracture disposed at a distance from the borehole.

[0033]FIG. 14B shows a top view of the formation in FIG. 14A.

DETAILED DESCRIPTION

[0034] In propagation logging, a high-frequency alternating current ofconstant intensity is sent through the transmitter antenna. Thealternating magnetic field created in the transmitter produces currents(eddy currents) in the formation surrounding the borehole. Since thealternating current in the transmitter is of constant frequency andamplitude, the magnitudes of the ground loop currents are directlyproportional to the formation conductivity. The voltage detected at thereceiver(s) is proportional to the magnitudes of the ground loopcurrents and, therefore, to the conductivity of the formation.

[0035] However, because the currents flow in circular loops coaxial withthe transmitter, if a receiver is disposed with its axis in a planeperpendicular to the axis of the transmitter, the eddy currents will notproduce any voltage in this receiver. Thus, in the absence ofinterference from the formation (e.g., in a homogeneous formation), onlythe receiver having an orientation non-perpendicular to that of thetransmitter would receive a voltage. Conventional propagation tools havemultiple transmitters and receivers paired up in various orientations.For example, in a triaxial propagation tool, there are threetransmitter-receiver antenna pairs arranged at orthogonal orientations.The receiver antennas are generally disposed at a distance from thetransmitter antennas. While the orientations of the receiver antennas ina conventional tool typically coincide with those of the transmitterantennas, one skilled in the art would appreciate that one or morereceiver antennas may be arranged on the same (or substantially similar)orthogonal axes but point to opposite directions (180° flip) withrespect to the corresponding transmitter antennas. In this case, thereceivers will register the same magnitudes of voltages but oppositesigns. The above description of current flow assumes that the formationis homogeneous isotropic. If the formation is anisotropic, the currentflows will be distorted.

[0036] Several prior art tools are available for investigatinganisotropic or inhomogeneous formations or formation boundaries. Forexample, U.S. Pat. No. 5,530,359 discloses a logging tool with multipletransmitter and receiver antennas for detecting locations of formationboundaries. U.S. Pat. No. 6,181,138 discloses a logging tool havingskewed antennas for directional resistivity measurements for azimuthalproximity detection of bed boundaries. On a related subject, U.S. patentapplication Ser. No. 10/113,132 filed on Mar. 29, 2002 by SchlumbergerTechnology Corporation entitled, “Directional ElectromagneticMeasurements Insensitive to Dip and Anisotropy”, discloses methods forformation logging using propagation tools that are insensitive toformation anisotropy. This application is assigned to the presentassignee.

[0037] While propagation tools have been used to detect formationresistivity and layering, i.e., dips and boundaries, these tools havenot been used to detect fractures. Compared with a formation layer, aformation fracture is very thin. A fracture may have a differentphysical property from the surrounding formation. In addition, fracturesoften cut across formation layers. Thus, a fracture creates aboundary/discontinuity in an otherwise homogenous layer. If the fractureis filled with hydrocarbons, which are non-conductive, the fracture actslike an insulating layer and is expected to have a dramatic impact onthe measured conductivity.

[0038] Embodiments of the invention are applicable to various fractures.A low conductivity fracture distorts, reduces, or interrupts the eddycurrents and, therefore, affects the voltages detected by propagationtools. The magnitudes of these effects depend on the distance of thefracture to the tool and its orientation relative to the tool.

[0039]FIG. 1 shows a planar fracture 2 embedded diagonally in an earthformation 1. A borehole 3 penetrates the earth formation 1perpendicularly to the horizontal plane 5 of the earth formation 1. Thefracture's orientation is defined by the normal 12 to the fracture'splane. The fracture's normal 12 makes an angle (α) with the longitudinalz-axis of the borehole 3. Projection 14 of the fracture's normal 12 ontoa plane parallel to the earth formation's horizontal plane 5 is at anangle (θ) with respect to the x-axis. In the art, the inclination of thefracture is usually defined by the fracture dip angle (Ψ) subtended bythe earth formation's horizontal plane 5 and the fracture plane.

[0040] As noted above, oil-filled fractures have dramatic effects on EMmeasurements. Therefore, a propagation tool with an ability to detectresponses in specific orientations (e.g., a triaxial tool having atriaxial transmitter and a triaxial receiver) can detect the presence offractures and their orientation. The techniques of the invention may beimplemented with any propagation tool capable of directional sensing.While this description uses a triaxial propagation tool to illustratemethods of the invention, one skilled in the art would appreciate thatother suitable tools (e.g., those having only TMD transmitter andreceiver antennas) may be used.

[0041]FIG. 2 shows a downhole logging system 15, which includes alogging tool 16 having a triaxial transmitter 19 and a triaxial receiver17, disposed in a borehole 3 that penetrates a formation 1. The triaxialreceiver 17 is arranged such that its axes or sensing directions (31_(x), 31 _(y), and 31 _(z)) are substantially parallel with the mutuallyorthogonal magnetic moments (33 _(x), 33 _(y), and 33 _(z)) of thetriaxial transmitter 19. The tool 16 is shown supported in the borehole3 by a logging cable 25 in the case of a wireline system or a drillstring 25 in the case of a LWD/LWT system. With a wireline tool, thetool 16 is raised and lowered in the borehole 3 by a winch 28, which iscontrolled by the surface equipment 21. Logging cable or drill string 25includes conductors or telemetry means 30 that link the downholeelectronics with the surface equipment 21 as known in the art. Downholeelectronics comprise a transmitter circuit 27 and a receiver circuit 29.The transmitter circuit 27 controls current flows through thetransmitter antennas (33 _(x), 33 _(y), 33 _(z)) to generate magneticmoments M_(x), M_(y), and M_(z) (not shown). The magnetic moments inturn produce eddy currents that flow in the earth formation 1surrounding the borehole 3. The eddy currents generate secondarymagnetic fields. The receiver circuit 29 detects voltages in thereceiver' antennas (31 _(x), 31 _(y), 31 _(z)) that are induced by thesecondary magnetic fields. The detected signals are communicated to thesurface equipment 21 for processing using known telemetry means.Alternatively, these signals may be processed in the tool 16, and theprocessed data are then transmitted to the surface. In some embodiments,the propagation tool 16 may include a motor (not shown) to rotate thetriaxial transmitter and the triaxial receiver in the azimuthaldirection.

[0042] The surface equipment 21 may be adapted to process the receivedvoltages as a function of depths and azimuthal angles of the tool 16.The voltages in the receiver antennas (31 _(x), 31 _(y), and 31 _(z))can be shown as vector voltages, the magnitudes and phases of whichdepend on the conductivity of the surrounding earth formation 1. Thereceived voltage is usually expressed as a complex signal (phasorvoltage).

[0043] In a homogeneous formation, the magnetic moments M_(x), M_(y) andM_(z) produced by the triaxial transmitter 19 only produce voltages inthe corresponding receivers in the same orientations. That is, when thetransmitter in the X-axis is energized, only the receiver aligned in theX direction detects a nonzero voltage. This is indicated as V_(xx).Similarly, when the Y transmitter is energized, only the Y receiverdetects a nonzero voltage, V_(yy), and the same is true for thetransmitter-receiver pair in the Z direction, V_(zz).

[0044]FIG. 3 illustrates a simple scenario in which the plane of thefracture coincides with a plane defined by two receiver axes (e.g.,y-z). If the fracture is filled with a fluid with a lower conductivity(e.g., an oil-filled fracture) than the fonnation, then the loopcurrents produced by the X transmitter, which flow in planes parallel tothe fracture plane, would not be significantly affected by the presenceof the fracture. Consequently, the coupling between the transmitter andreceiver in the X direction is substantially unaffected. Thus, thedetected V_(xx) is not substantially affected by the fracture. Incontrast, the currents produced by the Y or Z transmitters flow inplanes perpendicular to the fracture plane and the current loops flowthrough the fracture. As a result, the detected V_(yy) and V_(zz)voltages will be measurably reduced. However, the cross term voltages(i.e., V_(xy), V_(yx), V_(xz), V_(zx), V_(yz), and V_(zy)) remain zeroin this scenario because the presence of the fracture only affects themagnitudes of the generated currents but does not skew the currentloops.

[0045]FIG. 4 illustrate a scenario in which the plane of the fractureparallels the Z′ axis of the tool, but makes an angle (φ) with respectto the Y′ axis of the transmitter and receiver. This scenario occurswhen a tool is rotated by an angle (φ) from the situation illustrated inFIG. 3. In this second scenario, neither the X′ nor the Y′ axis of thetool is aligned with the fracture plane. As a result, the EM fieldsproduced by the X′ or Y′ transmitter will be “distorted” by the presenceof the low conductive fracture. Consequently, the cross terms (V_(xy),V_(yx)) will not be zero. The magnitudes of these cross terms depend onthe angle (φ).

[0046] If the tool is rotated as in an LWD/MWD operation, a series ofV_(xx), V_(yy), and V_(xy) voltages can be obtained as a function ofazimuthal angles (φ). The detected V_(xx), V_(yy), and V_(xy) voltagessignal responses will have sinusoidal modulations with respect to (φ).

[0047] The basic response of a TMD transmitter-receiver antenna pair toa resistive fracture in a 1 Ω-m formation is shown in FIG. 5. Theresponse represents a measurement with the parallel transverse antennasdisposed 30 inches (76.2 cm) apart and operating at 2 MHz. The angle (φ)is measured with respect to the fracture, and since this coupling hascos(2φ) sensitivity, responses are shown only in the interval 0-180°.Both the real and imaginary voltage components peak when the antenna'smagnetic dipoles are perpendicular to the fracture plane, since theinduced loop currents do not cross the fracture in such an orientation.TMD antennas with non-parallel transverse components have similarcos(2φ+φ₀) sensitivity with the phase reference (φ₀) equal to ½ of theangle closed by the transverse components of the TMD antennas.

[0048]FIG. 6 shows the building block for propagation directionalmeasurements with quadrant sensitivity according to an embodiment of theinvention. The layout is given in the x-y plane. The transmitter antennaT_(x) and receiver antennas R_(x,y) and R_(x,−y) are spaced apart alongthe longitudinal tool axis (represented as Z). The receivers R_(x,y) andR_(x,−y) may be collocated using saddle coil antennas or severaltilted-coil antennas as know in the art. Alternatively, the inventionmay be implemented with transverse receivers that are not collocatedalong the tool axis. FIG. 6 shows the receivers R_(x,y) and R_(x,−y) at+/−45° tilt angles (θ) in the transverse plane with respect to the toolaxis Z, but it should be noted that any tilt could be used and theangles do not have to be the same. The transmitter's magnetic dipolemoment and the receivers' axes are shown as vector arrows for ease ofillustration.

[0049]FIGS. 7A and 7B show the azimuthal dependence (angle φ) ofresponses to a 1-inch (2.54 cm) resistive fracture in a 1 Ω-m formationobtained with a propagation tool embodiment of the invention. FIG. 7Ashows the attenuation and 7B shows the phase shift. These responses wereproduced using a propagation tool with a transmitter-receiver spacing of28 inches (71.12 cm), XX and YY receivers spaced at 6 inches (15.24 cm)apart, and at an operating frequency of 2 MHz. The propagationmeasurement displays cos(2φ) sensitivity with a strong presence ofhigher order azimuthal dependence of responses. The azimuth φ=0corresponds to the tool position when the Y antenna is aligned with thefracture as depicted in FIG. 3.

[0050] The propagation measurements with antennas tilted in thetransverse plane, from FIGS. 7A-7B have responses (solid line)proportional to $\begin{matrix}{{M = {{\ln \frac{V_{x,y}}{V_{x,{- y}}}} = {{\ln \frac{V_{xx} + V_{xy}}{V_{xx} - V_{xy}}} = {{\ln ( {1 + \frac{2V_{xy}}{V_{xx} - V_{xy}}} )} \cong \frac{2V_{xy}}{V_{xx}}}}}},} & (1)\end{matrix}$

[0051] where the real part of the measurement M is proportional toattenuation and imaginary part is proportional to the phase shift. Itshould noted that V_(xx) in the denominator has the cos(2φ) dependencewhich causes appearance of cos(4φ), besides the cos(2φ) azimuthalvariation in the responses that is observed in FIGS. 7A-7B.

[0052] A way of extracting the responses with cos(2φ) and cos(4φ)azimuthal dependence from measurements with antenna configurationssimilar to that of FIG. 6 is presented in FIGS. 8A (Attenuation) and 8B(Phase Shift). FIGS. 8A-8B show responses to a 1 inch (2.54 cm)resistive fracture in a 1 Ω-m formation using a transmitter-receiverspacing of 28 inches (71.12 cm) and an operating frequency of 2 MHz.This embodiment of the invention combines the original measurement,noted as “meas 1”, with “meas 2”, which is “meas 1” shifted 90°. The sum“meas 1+meas 2” has cos(4φ) dependence in both attenuation and phaseshift, while the difference “meas 1−meas 2” has c(1-cos(4φ))sgn(sin(2φ)) dependence in attenuation and very close to cos(2φ)dependence of phase shift. Tool orientations where differentialmeasurement “meas 1−meas 2” is maximal are close to a 45° angle with thefracture. The azimuth φ=0 corresponds to the tool position when the Xantenna is aligned with the fracture.

[0053] The same responses from FIGS. 8A and 8B can be obtained using theembodiments of the invention shown in FIGS. 9 and 10. Both alternativeconfigurations use the concept of FIG. 6. The tool of FIG. 9 combinesthe responses of <T_(x), R_(x,−y), R_(x,y)> (meas 1) with <T_(y),R_(x,y), R_(x,y)> (meas 2). The tool of FIG. 10 measures attenuation andphase shift from transmitters T_(x) and T_(y) separately. The phaseshift measured with the tool of FIG. 10 is 180° from the measurementwith the tool of FIG. 9.

[0054] Another embodiment of the invention uses the TMD propagationmeasurements (XX and YY) to get responses with cos(2φ) and cos(4φ)dependence. Results from these measurements are presented in FIG. 11(Attenuation) and FIG. 12 (Phase Shift). These responses are to a 1-inch(2.54 cm) resistive fracture in a 1 Ω-m formation using atransmitter-receiver spacing of 28 inches (71.12 cm) and an operatingfrequency of 2 MHz. The XX measurement is “meas 1”, and “meas 2” is“meas 1” shifted 90 degrees (YY). The sum and difference attenuationresponses include cos(4φ) and cos(2φ) dependence (FIG. 11). On the otherhand, the phase shift responses and the sum “meas 1+meas 2” responsehave cos(2φ) dependence and the difference “meas 1−meas 2” has close tocos(4φ) dependence. Fracture orientation is at azimuth when “meas 1+meas2” is maximal. The azimuth φ=0 corresponds to the tool position when theX antenna is aligned with the fracture.

[0055] Another aspect of the invention applies harmonic analysis to TMDantenna configurations that entail transverse components. Although theraw voltage response of TMD antennas to a resistive fracture has cos(2φ)sensitivity, the voltage magnitude and phase have higher harmonics. Theharmonic content for the signals from FIG. 5 is shown in FIG. 13. Bymonitoring the second harmonic of the voltage signal, one can estimatethe fracture orientation knowing that the signal is maximal when theantennas are not aligned with the fracture. The effects of boreholeeccentering as well as nearby boundaries can cause the appearance of asecond harmonic. However, the second harmonic due to fractures istypically more significant. Measurements from other couplings (e.g.axial and cross-dipole measurements) may be used to remove or correctfor ambiguity in defining the fracture orientation.

[0056] For a given channel (frequency f, transmitter t, receiver r)voltage measurement, a fitting algorithm (FFT) will produce coefficientsa_(RE i), b_(RE i), a_(IM i), b_(IM i): $\begin{matrix}{\begin{matrix}{{{Re}\{ {V( {f,t,r} )} \}} = {a_{RE0} + {\sum\limits_{k = 1}^{N}\quad \{ {{a_{REk}{\cos ( {k\quad \varphi} )}} + {b_{REk}{\sin ( {k\quad \varphi} )}}} \}}}} \\{{{Im}\{ {V( {f,t,r} )} \}} = {a_{IM0} + {\sum\limits_{k = 1}^{N}\quad \{ {{a_{IMk}{\cos ( {k\quad \varphi} )}} + {b_{IMk}{\sin ( {k\quad \varphi} )}}} \}}}}\end{matrix},} & (2)\end{matrix}$

[0057] where φ is the angle with respect to the reference antennaorientation. The tan⁻¹ of the second harmonic coefficient ratio isdetermined by the fracture orientation. The fracture orientation can beobtained by averaging the value from the real (Re) and imaginary (Im)part of the voltage second harmonic: $\begin{matrix}{{\varphi_{frac}( {f,t,r} )} = {\frac{1}{4}{( {{\tan^{- 1}\frac{b_{RE2}}{a_{RE2}}} + {\tan^{- 1}\frac{b_{IM2}}{a_{IM2}}}} ).}}} & (3)\end{matrix}$

[0058] Note that for each individual component, there is ½ in front oftan⁻¹ because the second harmonic is used. Though the previousdescription focused on the basic antenna pair configuration, it shouldbe understood that the present invention is not limited to the use ofany particular number of antennas or antenna pairings.

[0059] When using a plurality of antennas, a summation is performed andaveraged to obtain the fracture orientation: $\begin{matrix}{{\frac{1}{N_{rec}}{\sum\limits_{i = 1}^{Nrec}\quad {\varphi_{frac}( {f,t,{ri}} )}}},} & (4)\end{matrix}$

[0060] where (f, t, ri) corresponds to a measurement at the ith receiverantenna and N_(rec) is the number of receiver antennas.

[0061] The fracture orientation can also be determined, using Equation(3), from the couplings between a TMD transmitter and two TMD receivers(such as shown in FIG. 6) by averaging the couplings as follows:

½{φ_(frac)(f, t, r1)+φ_(frac)(f, t, r2)},  (5)

[0062] where (f, t, r1) corresponds to the measurement at one receiverand (f, t, r2) to that at the other receiver. Extension to morereceivers is straightforward. In this embodiment, the harmonic fittingis performed after the voltage signals are measured.

[0063] For simplicity, the above analysis was shown with the plane ofthe fracture cutting through the borehole. Similar results are obtainedif the plane of the fracture parallels the Z axis but is disposed at adistance from the borehole as shown in FIGS. 14A and 14B. FIG. 14A showsa perspective view of a fracture 2 cutting through an earth formation 1such that the longitudinal axis of the borehole 3 parallels the fractureplane. FIG. 14B shows a top view of the fracture 2 and the borehole 3shown in FIG. 14A.

[0064] In this case, the angular dependence of the cross term voltages,V_(xy) and V_(yx), remains the same. However, the magnitudes of angularmodulations on various terms, V_(xx), V_(yy), V_(zz), V_(xy), andV_(yx), will be smaller because the effects of the fracture are moreremote. In fact, the magnitudes of angular modulations in suchmeasurements may be used to predict the distance between the fractureplane and the borehole. If several such measurements are obtained as afunction of axial depth, the distances between the fracture plane andthe borehole at various axial depths may be used to determine the tiltof the fracture plane relative to the Z-axis.

[0065] It will be apparent to those skilled in the art that thisinvention may be implemented by programming one or more suitablegeneral-purpose computers having appropriate hardware. The programmingmay be accomplished through the use of one or more program storagedevices readable by the computer processor and encoding one or moreprograms of instructions executable by the computer for performing theoperations described above. The program storage device may take the formof, e.g., one or more floppy disks; a CD ROM or other optical disk; amagnetic tape; a read-only memory chip (ROM); and other forms of thekind well-known in the art or subsequently developed. The program ofinstructions may be “object code,” i.e., in binary form that isexecutable more-or-less directly by the computer; in “source code” thatrequires compilation or interpretation before execution; or in someintermediate form such as partially compiled code. The precise forms ofthe program storage device and of the encoding of instructions areimmaterial here. Thus these processing means may be implemented in thesurface equipment, in the tool, or shared by the two as known in theart.

[0066] Advantages of the present invention include convenient techniquesfor detecting the presence and orientation of formation fractures. Itwill be appreciated by those skilled in the art that the methods of theinvention may be used with a wireline tool, an LWD/MWD tool, or an LWTtool. It will also be appreciated that the antennas used to implementthe invention may be constructed using any techniques known in the art.For the purposes of this specification it will be clearly understoodthat the word “comprising” means “including but not limited to”, andthat the word “comprises” has a corresponding meaning.

What is claimed is:
 1. A method for locating a fracture in an earthformation using a propagation tool disposed in a borehole traversing theformation, the tool having a longitudinal axis, comprising: (a)transmitting electromagnetic energy from a transmitter antenna disposedon the propagation tool with its magnetic moment at an angle withrespect to the longitudinal tool axis; (b) measuring voltage signalsdetected at a plurality of receiver antennas disposed on the propagationtool with their axes at an angle with respect to the longitudinal toolaxis and oriented in different directions from one another, the voltagesignals being related to the transmitted electromagnetic energy; (c)associating the measured voltage signals with a plurality of azimuthalangles; and (d) shifting at least one of the measured voltage signals bya predetermined angle and processing the shifted and unshifted signalsto locate the fracture.
 2. The method of claim 1, wherein the measuredvoltage signals relate to a phase difference or a magnitude ratio of thesignals detected by said receiver antennas.
 3. The method of claim 2,wherein step (d) includes determining signal harmonics from the measuredvoltage signals.
 4. The method of claim 3, wherein step (d) includesperforming a subtraction or addition between the shifted and unshiftedsignals.
 5. The method of claim 4, wherein step (d) includes shifting atleast one of the measured signals by 90 degrees.
 6. The method of claim4, wherein the transmitter antenna is disposed on the tool with itsmagnetic moment oriented in a transverse plane with respect to thelongitudinal tool axis.
 7. The method of claim 4, wherein a first pairof receiver antennas are disposed on the tool with their axes projectedin a transverse plane with respect to the longitudinal tool axis andorientated in different directions from one another.
 8. The method ofclaim 7, wherein the transmitter antenna is disposed on the tool withits magnetic moment oriented in a transverse plane with respect to thelongitudinal tool axis.
 9. The method of claim 8, wherein step (d)includes determining an orientation of the fracture relative to an axisof an antenna disposed on the tool.
 10. The method of claim 9, whereinstep (d) includes shifting at least one of the measured signals by 90degrees.
 11. The method of claim 8, wherein the tool comprises a secondtransmitter antenna disposed thereon with its magnetic moment orientedat an angle with respect to the longitudinal tool axis and perpendicularto the magnetic moment of the first transmitter antenna.
 12. The methodof claim 11, wherein step (b) comprises measuring the voltage signalscorresponding to the electromagnetic energy transmitted from the firstand second transmitter antennas at the first pair of receiver antennas.13. The method of claim 12, wherein step (d) includes determining anorientation of the fracture relative to an axis of an antenna disposedon the tool.
 14. The method of claim 11, wherein a second pair ofreceiver antennas are disposed on the tool with their axes projected ina transverse plane with respect to the longitudinal tool axis andoriented in different directions from one another.
 15. The method ofclaim 14, wherein step (b) comprises measuring the voltage signalscorresponding to the electromagnetic energy transmitted from the firstand second transmitter antennas at the first and second pair of receiverantennas.
 16. The method of claim 4, wherein step (b) comprisesmeasuring a voltage signal detected at a receiver antenna disposed onthe tool with its axis parallel to and substantially aligned with themagnetic moment of the transmitter antenna.
 17. The method of claim 16,wherein the parallel and aligned transmitter and receiver antennas areoriented in an X-coordinate direction or in a Y-coordinate direction.18. The method of claim 17, wherein step (d) includes determining anorientation of the fracture relative to an axis of an antenna disposedon the tool.
 19. A system for locating a fracture in an earth formationcomprising: a propagation tool having a longitudinal axis and adaptedfor disposal within a borehole traversing the formation; a transmitterantenna disposed on the tool with its magnetic moment at an angle withrespect to the tool axis; a plurality of receiver antennas disposed onthe tool with their axes at an angle with respect to the tool axis andoriented in different directions from one another, the antennas adaptedto detect voltage signals associated with electromagnetic energytransmitted by the transmitter antenna; processing means to measure thevoltage signals detected by said receiver antennas; processing means toassociate the measured voltage signals with a plurality of azimuthalangles; and processing means to shift at least one of the measuredvoltage signals by a predetermined angle and to process the shifted andunshifted signals to locate the fracture.
 20. The system of claim 19,wherein the processing means to measure the detected voltage signalscomprises means to measure a phase difference or a magnitude ratio ofthe detected voltage signals.
 21. The system of claim 20, wherein theprocessing means to measure the detected voltage signals furthercomprises means to determine signal harmonics from the detected voltagesignals.
 22. The system of claim 21, wherein the processing means toprocess the shifted and unshifted signals comprises means to perform asubtraction or addition between the shifted and unshifted signals. 23.The system of claim 22, wherein the processing means to shift at leastone of the measured signals comprises means to shift at least one of themeasured signals by 90 degrees.
 24. The system of claim 22, wherein thetransmitter antenna is disposed on the tool with its magnetic momentoriented in a transverse plane with respect to the longitudinal toolaxis.
 25. The system of claim 22, the tool comprising a first pair ofreceiver antennas disposed thereon with their axes projected in atransverse plane with respect to the tool axis and orientated indifferent directions from one another.
 26. The system of claim 25,wherein the transmitter antenna is disposed on the tool with itsmagnetic moment oriented in a transverse plane with respect to thelongitudinal tool axis.
 27. The system of claim 26, the tool comprisinga second transmitter antenna disposed thereon with its magnetic momentoriented at an angle with respect to the tool axis and perpendicular tothe magnetic moment of the first transmitter antenna.
 28. The system ofclaim 27, the tool comprising a second pair of receiver antennasdisposed thereon with their axes projected in a transverse plane withrespect to the tool axis and oriented in different directions from oneanother.
 29. The system of claim 28, wherein the processing means toprocess the shifted and unshifted signals comprises means to determinean orientation of the fracture relative to an axis of an antennadisposed on the tool.
 30. The system of claim 22, the tool comprising areceiver antenna disposed thereon with its axis parallel to andsubstantially aligned with the magnetic moment of the transmitterantenna.
 31. The system of claim 31, wherein the parallel and alignedtransmitter and receiver antennas are oriented in an X-coordinatedirection or in a Y-coordinate direction.
 32. A method for locating afracture in an earth formation penetrated by a borehole, comprising: (a)moving a propagation tool in the borehole, the tool having alongitudinal axis and including a first transmitter antenna disposedthereon with its magnetic moment at a right angle to the tool axis and aplurality of receiver antennas disposed thereon with their axes at rightangles to the tool axis; (b) transmitting electromagnetic energy usingthe first transmitter antenna; (c) measuring voltage signals detected atthe plurality of receiver antennas, the signals being related to thetransmitted electromagnetic energy; (d) associating the measured signalswith a plurality of azimuthal angles; (e) shifting at least one of themeasured signals by a predetermined angle; and (f) locating the fractureusing the shifted and unshifted signals.
 33. The method of claim 32,wherein step (c) includes measuring a phase difference or a magnituderatio of the voltage signals detected at a first pair of receiverantennas disposed on the tool with their axes at right angles to oneanother.
 34. The method of claim 33, wherein step (e) includes shiftingat least one of the measured signals by 90 degrees and respectivelyadding or subtracting the shifted signal to or from an unshifted signal.35. The method of claim 34, wherein step (f) includes determining anorientation of the fracture relative to an axis of an antenna disposedon the tool.
 36. The method of claim 35, wherein step (c) includesmeasuring the voltage signals corresponding to electromagnetic energytransmitted from the first transmitter antenna and from a secondtransmitter antenna disposed on the tool with its magnetic moment at anangle with respect to the tool axis and perpendicular to the magneticmoment of the first transmitter antenna.
 37. The method of claim 36,wherein step (c) includes measuring the voltage signals corresponding toelectromagnetic energy transmitted from the first and second transmitterantennas at the first pair of receiver antennas and at a second pair ofreceiver antennas disposed on the tool with their axes at right anglesto one another.
 38. The method of claim 35, wherein step (c) includesmeasuring a voltage signal detected at a receiver antenna oriented in anX-coordinate direction or in a Y-coordinate direction, the measuredsignal corresponding to electromagnetic energy transmitted from thefirst transmitter antenna oriented in the same respective direction. 39.A method for locating a fracture in an earth formation using a loggingtool disposed in a borehole traversing the formation, the tool having alongitudinal axis, comprising: (a) transmitting electromagnetic energyfrom a transmitter antenna disposed on the tool with its magnetic momentat an angle with respect to the longitudinal tool axis; (b) measuringvoltage signals detected with a receiver antenna disposed on the toolwith its axis at an angle with respect to the longitudinal tool axis,the voltage signals being related to the transmitted electromagneticenergy; (c) determining a second harmonic associated with the measuredvoltage signals; and (d) performing a calculation on the second harmonicto locate the fracture.
 40. The method of claim 39, wherein step (d)includes averaging values computed from real and imaginary parts of thesecond harmonic.
 41. The method of claim 40, wherein step (d) includescalculating the following equation:${{\varphi_{frac}( {f,t,r} )} = {\frac{1}{4}( {{\tan^{- 1}\frac{b_{RE2}}{a_{RE2}}} + {\tan^{- 1}\frac{b_{IM2}}{a_{IM2}}}} )}},$

where (f, t, r) corresponds to a voltage signal measurement at frequencyf transmitter antenna t, and receiver antenna r; φ is the angle of thefracture relative to an axis of the measurement antenna; and a_(RE2),b_(RE2), a_(IM2), b_(IM2) are coefficients corresponding to real andimaginary parts of the second harmonic.
 42. The method of claim 40,wherein the transmitter and receiver antennas are disposed on the toolwith their axes parallel to one another and oriented in a transverseplane with respect to the longitudinal tool axis.
 43. The method ofclaim 39, wherein step (b) comprises measuring voltage signals detectedwith a plurality of receiver antennas disposed on the tool each with itsaxis at an angle with respect to the longitudinal tool axis.
 44. Themethod of claim 43, wherein step (d) includes averaging values computedfrom real and imaginary parts of the second harmonic.
 45. The method ofclaim 44, wherein step (d) includes calculating the following equation:${\varphi_{frac}( {f,t,{ri}} )} = {\frac{1}{4}( {{\tan^{- 1}\frac{b_{RE2}}{a_{RE2}}} + {\tan^{- 1}\frac{b_{IM2}}{a_{IM2}}}} )}$

where (f, t, ri) corresponds to a voltage signal measurement atfrequency f transmitter antenna t, and receiver antenna ri; φ is theangle of the fracture relative to an axis of the measurement antenna;and a_(RE2), b_(RE2), a_(IM2), b_(IM2) are coefficients corresponding toreal and imaginary parts of the second harmonic.
 46. The method of claim45, wherein step (d) includes calculating the following equation:$\frac{1}{N_{rec}}{\sum\limits_{i = 1}^{Nrec}\quad {\varphi_{frac}( {f,t,{ri}} )}}$

where (f, t, ri) corresponds to a measurement at the ith receiverantenna and N_(rec) is the number of receiver antennas.
 47. The methodof claim 43, wherein the transmitter and receiver antennas are disposedon the tool with their axes parallel to one another and oriented in atransverse plane with respect to the longitudinal tool axis.
 48. Asystem for locating a fracture in an earth formation comprising: alogging tool having a longitudinal axis and adapted for disposal withina borehole traversing the formation; a transmitter antenna disposed onthe tool with its magnetic moment at an angle with respect to the toolaxis; a receiver antenna disposed on the tool with its axis at an anglewith respect to the tool axis, the antenna adapted to detect voltagesignals associated with electromagnetic energy transmitted by thetransmitter antenna; processing means to determine a second harmonicassociated with voltage signals detected with the receiver antenna; andprocessing means to perform a calculation on the second harmonic tolocate the fracture.
 49. The system of claim 48, wherein the processingmeans to perform a calculation on the second harmonic comprises means toaverage values computed from real and imaginary parts of the secondharmonic.
 50. The system of claim 49, wherein the processing means toperform a calculation on the second harmonic comprises means tocalculate the following equation:${\varphi_{frac}( {f,t,r} )} = {\frac{1}{4}( {{\tan^{- 1}\frac{b_{RE2}}{a_{RE2}}} + {\tan^{- 1}\frac{b_{IM2}}{a_{IM2}}}} )}$

where (f, t, r) corresponds to a voltage signal measurement at frequencyf transmitter antenna t, and receiver antenna r; φ is the angle of thefracture relative to an axis of the measurement antenna; and a_(RE2),b_(RE2), a_(IM2), b_(IM2) are coefficients corresponding to real andimaginary parts of the second harmonic.
 51. The system of claim 48,wherein the transmitter and receiver antennas are disposed on the toolwith their axes parallel to one another and oriented in a transverseplane with respect to the longitudinal tool axis.
 52. The system ofclaim 48, further comprising a second receiver antenna disposed on thetool with its axis at an angle with respect to the tool axis and saidprocessing means adapted to determine the second harmonic using thevoltage signals detected with said receiver antennas.
 53. The system ofclaim 52, wherein the processing means to perform a calculation on thesecond harmonic comprises means to average real and imaginary parts ofthe second harmonic.
 54. The system of claim 53, wherein the processingmeans to perform a calculation on the second harmonic comprises means tocalculate the following equation:${\varphi_{frac}( {f,t,{ri}} )} = {\frac{1}{4}( {{\tan^{- 1}\frac{b_{RE2}}{a_{RE2}}} + {\tan^{- 1}\frac{b_{IM2}}{a_{IM2}}}} )}$

where (f, t, ri) corresponds to a voltage signal measurement atfrequency f transmitter antenna t, and receiver antenna ri; φ is theangle of the fracture relative to an axis of the measurement antenna;and a_(RE2), b_(RE2), a_(IM2), b_(IM2) are coefficients corresponding toreal and imaginary parts of the second harmonic.
 55. The system of claim54, wherein the processing means to perform a calculation on the secondharmonic comprises means to calculate the following equation:$\frac{1}{N_{rec}}{\sum\limits_{i = 1}^{Nrec}\quad {\varphi_{frac}( {f,t,{ri}} )}}$

where (f, t, ri) corresponds to a measurement at the ith receiverantenna and N_(rec) is the number of receiver antennas.
 56. The systemof claim 52, wherein the transmitter and receiver antennas are disposedon the tool with their axes parallel to one another and oriented in atransverse plane with respect to the longitudinal tool axis.